历史与综述

We examine a measure of individual student gain by preservice elementary teachers, related to Richard Hakes use of mean gain in the study of reform classes in undergraduate physics. The gain statistic assesses the amount individual students…

The architecture has its basis in a dialectic search of new choices of representation. We deal with the form on the contemporary architecture under two approaches: expression and content. We examine how mathematical principles based on…

This paper traces the history of compactness from the original motivating questions, through the development of the definition, to a generalization of sequential compactness in terms of nets and filters.

Yet more candidates are proposed for inclusion in the Encyclopedia of Triangle Centers. Our focus is entirely on simple calculations.

One of the basics of calculus is the following proposition: If $F$ and $G$ are antiderivatives of two real functions $f$ and $g$ resp., then an antiderivative of $\lambda f+g$ is $\lambda F + G$. It may be surprising that such systematic an…

The Pythagorean formula is one of the most popular ways to measure the true ability of a team. It is very easy to use, estimating a team's winning percentage from the runs they score and allow. This data is readily available on standings…

We present a proof of the existence of real eigenvalues of real symmetric matrices which does not rely on any limit or compactness arguments, but only uses the notions of "sup", "inf".

The purpose of this note is to discuss a few lines appearing in the work of late Fantappi\`e. They concern the proof of rigidity of a specific real semisimple Lie algebra: ${\mathfrak O}(4,1)$. Our intention is to discuss to what extent…

This paper describes a collaboration between a mathematician and a compositionist who developed a sequence of collaborative writing assignments for calculus. This sequence of developmentally-appropriate assignments presents peer review as a…

Postgraduate taught degrees in financial mathematics have been booming in popularity in the UK for the last 20 years. The fees for these courses are considerably higher than other comparable masters-level courses. Why? Vendors stipulate…

On the 500th anniversary of Albrecht D\"urer's copperplate engraving Melencolia I, we invite readers to join in a time-honored "party game" that has attracted art historians and scientists for many years: guessing the nature and meaning of…

We present initially the motivation, definition and basic properties of differential equations with proportional delay. In the last Section we present open problems.

This paper presents a survey of the khipu-based enumeration system of the Incas. In this system, different knots are tied together and they are attached to a primary cord. The numerical basis of the khipu system is well understood but more…

We discuss a completely forgotten work of the geologist G.F. Becker on the ideal isotropic nonlinear stress-strain function. In doing this we provide the original paper from 1893 newly typeset in LaTeX and with corrections of typographical…

Let $P_1,P_2,P_3$ be three given points in $\mathbf{R}^2$, and $P$ be an arbitrary point in $\mathbf{R}^2$. The classical Fermat's problem to Torricelli asks for the location of the point $P$ such that $|PP_1|+|PP_2|+|PP_3|$ is a minimum.…

We give a geometric proof of the Routh's theorem for tetrahedra.

In the present work it is shown, by an examination of the Platonic dialogues Theaetetus, Sophistes, Politicus, and Philebus, that (a) a Platonic Idea is the philosophic analogue of a pair of lines incommensurable in length only, (b) the…

The use of technology in schools has been one of the most debated topics around mathematics education. In some countries there is a huge investment, in others there is a down-scaling. Malaysia decided in 2013 to put its 10 million students…

We review the state approach to toss juggling and extend the approach to spin juggling, a new concept. We give connections to current research on random juggling and describe a professional-level juggling performance that further…

This is the first of the proposed sets of notes to be published in the website Gonit Sora (http://gonitsora.com). The notes will hopefully be able to help the students to learn their subject in an easy and comprehensible way. These notes…